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2023-12-11Zeitschriftenartikel DOI: 10.18452/28467
Cohomology of semisimple local systems and the decomposition theorem
dc.contributor.authorWei, Chuanhao
dc.contributor.authorYang, Ruijie
dc.date.accessioned2024-04-10T09:37:18Z
dc.date.available2024-04-10T09:37:18Z
dc.date.issued2023-12-11none
dc.identifier.urihttp://edoc.hu-berlin.de/18452/29114
dc.description.abstractIn this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we construct a generalized Weil operator from the complex conjugate of the cohomology of a semisimple local system to the cohomology of its dual local system, which is functorial with respect to smooth restrictions. This operator allows us to study the Poincaré pairing, usually not positive definite, in terms of a positive definite Hermitian pairing. On the other hand, we prove a global invariant cycle theorem for semisimple local systems. As an application, we give a new proof of Sabbah’s Decomposition Theorem for the direct images of semisimple local systems under proper algebraic maps, by adapting the method of de Cataldo-Migliorini, without using the category of polarizable twistor modules. This answers a question of Sabbah.eng
dc.language.isoengnone
dc.publisherHumboldt-Universität zu Berlin
dc.rights(CC BY 4.0) Attribution 4.0 Internationalger
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectSemisimple local systemseng
dc.subjectDecomposition theoremeng
dc.subjectHodge structureeng
dc.subjectTwistor structureeng
dc.subjectPolarizationeng
dc.subject14C30eng
dc.subject32S60eng
dc.subject.ddc510 Mathematiknone
dc.titleCohomology of semisimple local systems and the decomposition theoremnone
dc.typearticle
dc.identifier.urnurn:nbn:de:kobv:11-110-18452/29114-9
dc.identifier.doihttp://dx.doi.org/10.18452/28467
dc.type.versionpublishedVersionnone
local.edoc.pages62none
local.edoc.type-nameZeitschriftenartikel
local.edoc.container-typeperiodical
local.edoc.container-type-nameZeitschrift
dc.description.versionPeer Reviewednone
dc.identifier.eissn1420-9020
dcterms.bibliographicCitation.doi10.1007/s00029-023-00895-2
dcterms.bibliographicCitation.journaltitleSelecta mathematicanone
dcterms.bibliographicCitation.volume30none
dcterms.bibliographicCitation.issue1none
dcterms.bibliographicCitation.articlenumber5none
dcterms.bibliographicCitation.originalpublishernameBirkhäusernone
dcterms.bibliographicCitation.originalpublisherplaceBerlinnone
bua.departmentMathematisch-Naturwissenschaftliche Fakultätnone

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